I don't believe so. Dogs are very protective over there pups and I think that no matter how hungry they are they wouldn't hurt them.
Will a mother dog eat her new born pups if she is hungry enough?
never..
She might also eat new born pups if she gave birth to too many of them, I believe.
But I don't believe she'll eat them just purely out of hunger. Like the other answerer stated, there'd probably have to be something wrong with a new born pup if the mother were to eat it.